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International Journal for Uncertainty Quantification
Главный редактор: Habib N. Najm (open in a new tab)
Ассоциированный редакторs: Dongbin Xiu (open in a new tab) Tao Zhou (open in a new tab)
Редактор-основатель: Nicholas Zabaras (open in a new tab)

Выходит 6 номеров в год

ISSN Печать: 2152-5080

ISSN Онлайн: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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EFFICIENT APPROXIMATION OF HIGH-DIMENSIONAL EXPONENTIALS BY TENSOR NETWORKS

Том 13, Выпуск 1, 2023, pp. 25-51
DOI: 10.1615/Int.J.UncertaintyQuantification.2022039164
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Краткое описание

In this work a general approach to compute a compressed representation of the exponential exp (h) of a high-dimensional function h is presented. Such exponential functions play an important role in several problems in uncertainty quantification, e.g., the approximation of log-normal random fields or the evaluation of Bayesian posterior measures. Usually, these high-dimensional objects are numerically intractable and can only be accessed pointwise in sampling methods. In contrast, the proposed method constructs a functional representation of the exponential by exploiting its nature as a solution of a partial differential equation. The application of a Petrov−Galerkin scheme to this equation provides a tensor train representation of the solution for which we derive an efficient and reliable a posteriori error estimator. This estimator can be used in conjunction with any approximation method and the differential equation may be adapted such that the error estimates are equivalent to a problem-related norm. Numerical experiments with log-normal random fields and Bayesian likelihoods illustrate the performance of the approach in comparison to other recent low-rank representations for the respective applications. Although the present work considers only a specific differential equation, the presented method can be applied in a more general setting. We show that the proposed method can be used to compute compressed representations of φ(h) for any holonomic function φ.

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